Japanese Multiplication Method

The Japanese have a curious and easy Multiplication method which is really intriguing.

I call it 'The Chopstick Multiplication'.

Suppose you want to calculate

367 X 213=?

Here is what you do.

1.       Refer Fig-1 and draw drawings corresponding to each digit in 367 as shown from Bottom-left to Top-Right.  

Fig-1

2.       Next on top of the lines drawn in Fig-1, refer Fig-2 and draw lines corresponding to 213 from Left-Top to Bottom-Right.  

Fig-2

3.       These two sets of lines will intersect and form 5 Intersection sets. Intersection-1 to Intersection-5.

4.       Start from the bottom right and in the first Intersection set, we find that there are 21 points.  Take 1 from 21 and carryover 2 to add to the number of points in the next Intersection Set, Intersection Set-2.  (Refer Fig-3)  

Fig-3

5.       Now count the intersection points in Intersection Set-2 and add the carryover from previous Intersection Set-1 to this.  Again take the units place number and carryover the remaining part to the next Intersection Set and so on. (Refer Fig-4,5,6,7)

Fig-4

   

Fig-5

Fig-6

Fig-7

6.       Write down the digits we had taken at each intersection next to each other starting from Intersection-5 on extreme left to Intersection-1 on extreme right. And we get

** 78171 **

Which is the Answer